Interface coupling effects on Rayleigh–Taylor and Faraday instabilities in granular suspensions under oscillatory forcing

Abstract

This study investigates how interface coupling effect affects the sedimentation dynamics of finite-thickness granular suspensions under both constant gravity and oscillatory accelerations. Through Euler–Lagrange simulations, we examine the evolution of Rayleigh–Taylor instability (RTI) at the lower interface. Under constant gravity, reducing suspension thickness, thereby intensifying interface coupling effects, suppresses the growth rate of RTI while increasing the dominant wavenumber. Under oscillatory acceleration, two competing mechanisms emerge: while reduced thickness inherently inhibits RTI growth in the absence of oscillation, it simultaneously weakens oscillations’ stabilizing effect. This competition leads to a reversal of behavior observed under constant gravity, wherein high-amplitude oscillations cause thinner suspensions to exhibit more rapid instability growth than thicker layers. Linear stability analysis captures this reversal and matches numerical results well. It further demonstrates that, due to the attenuated effect of oscillation-induced stabilization, increasing oscillation amplitude inevitably induces growth rate inversions from high to low wavenumbers in thinner suspensions; nevertheless, these suspensions consistently maintain higher dominant wavenumbers. Additionally, granular suspensions can also develop Faraday instability (FI) at the upper interface, with its dominant wavenumbers increasing with oscillation frequency, though this increase diminishes particle resolution at interfaces, leading to reduced consistency between theoretical and numerical results.